Pages

Monday, July 23, 2018

Evidence for modified gravity is now evidence against it.

It’s day 12,805 in the war between modified gravity and dark matter. That’s counting the days since the publication of Mordehai Milgrom’s 1983 paper. In this paper he proposed to alter Einstein’s theory of general relativity rather than conjecturing invisible stuff.

Dark matter, to remind you, are hypothetical clouds of particles that hover around galaxies. We can’t see them because they neither emit nor reflect light, but we do notice their gravitational pull because it affects the motion of the matter that we can observe. Modified gravity, on the other hand, posits that normal matter is all there is, but the laws of gravity don’t work as Einstein taught us.

Which one is right? We still don’t know, though astrophysicists have been on the case since decades.

Ruling out modified gravity is hard because it was invented to fit observed correlations, and this achievement is difficult to improve on. The idea which Milgrom came up with in 1983 was a simple model called Modified Newtonian Dynamics (MOND). It does a good job fitting the rotation curves of hundreds of observed galaxies, and in contrast to particle dark matter this model requires only one parameter as input. That parameter is an acceleration scale which determines when the gravitational pull begins to be markedly different from that predicted by Einstein’s theory of General Relativity. Based on his model, Milgrom also made some predictions which held up so far.

That’s pretty amazing given that two months ago modified gravity worked just fine for galaxies. It’s even more amazing once you notice that they ruled out modified gravity using the same data from which McGaugh et al extracted the universal acceleration scale that’s evidence for modified gravity.

Shown on the vertical axis is their best-fit parameter for the (log of) the acceleration scale. On the horizontal axis are the individual galaxies. The authors have sorted the galaxies so that the best-fit value is monotonically increasing from left to right, so the increase is not relevant information. Relevant is that if you compare the error-margins marked by the colors, then the best-fit value for the galaxies on the very left side of the plot are incompatible with the best-fit values for the galaxies on the very right side of the plot.

So what the heck is going on?

A first observation is that the two studies don’t use the same data analysis. The main difference is the priors for the distribution of the parameters which are the acceleration scale of modified gravity and the stellar mass-to-light ratio. Where McGaugh et al use Gaussian priors, Rodrigues et al use flat priors over a finite bin. The prior is the assumption you make for what the likely distribution of a parameter is, which you then feed into your model to find the best-fit parameters. A bad prior can give you misleading results.

Example: Suppose you have an artificially intelligent infrared camera. One night it issues an alert: Something’s going on in the bushes of your garden. The AI tells you the best fit to the observation is a 300-pound hamster, the second-best fit is a pair of humans in what seems a peculiar kind of close combat. Which option do you think is more likely?

I’ll go out on a limb and guess the second. And why is that? Because you probably know that 300-pound hamsters are somewhat of a rare occurrence, whereas pairs of humans are not. In other words, you have a different prior than your camera.

Back to the galaxies. As we’ve seen, if you start with an unmotivated prior, you can end up with a “best fit” (the 300 pound hamster) that’s unlikely for reasons your software didn’t account for. At the very least, therefore, you should check that whatever the resulting best-fit distribution of your parameters is doesn’t contradict other data. The Rodrigues et al analysis hence raises the concern that their best-fit distribution for the stellar mass-to-light ratio doesn’t match commonly observed distributions. The McGaugh paper on the other hand starts with a Gaussian prior, which is a reasonable expectation, and hence their analysis makes more physical sense.

Having said this though, it turns out the priors don’t make much of a difference for the results. Indeed, for what the numbers are concerned the results in both papers are pretty much the same. What differs is the conclusion the authors draw from it.

Let me tell you a story to illustrate what’s going on.
Suppose you are Isaac Newton and an apple just banged on your head. “Eureka,” you shout and postulate that the gravitational potential fulfils the Poisson-equation.* Smart as you are, you assume that the Earth is approximately a homogeneous sphere, solve the equation and find an inverse-square law. It contains one free parameter which you modestly call “Newton’s constant.”

You then travel around the globe, note down your altitude and measure the acceleration of a falling test-body. Back home you plot the results and extract Newton’s constant (times the mass of the Earth) from the measurements. You find that the measured values cluster around a mean. You declare that you have found evidence for a universal law of gravity.

Or have you?

A week later your good old friend Bob knocks on the door. He points out that if you look at the measurement errors (which you have of course recorded), then some of the measurement results are incompatible with each other at five sigma certainty. There, Bob declares, I have ruled out your law of gravity.

Same data, different conclusion. How does this make sense?

“Well,” Newton would say to Bob, “You have forgotten that besides the measurement uncertainty there is theoretical uncertainty. The Earth is neither homogeneous nor a sphere, so you should expect a spread in the data that exceeds the measurement uncertainty.” – “Ah,” Bob says triumphantly, “But in this case you can’t make predictions!” – “Sure I can,” Newton speaks and points to his inverse square law, “I did.” Bob frowns, but Newton has run out of patience. “Look,” he says and shoves Bob out of the door, “Come back when you have a better theory than I.”

Back to 2018 and modified gravity. Same difference. In the Rodrigues et al paper, the authors rule out that modified gravity’s one-parameter law fits all disk galaxies in the sample. This shouldn’t come as much of a surprise. Galaxies aren’t disks with bulges any more than the Earth is a homogeneous sphere. It’s such a crude oversimplification it’s remarkable it works at all.

Indeed, it would be an interesting exercise to quantify how well modified gravity does in this set of galaxies compared to particle dark matter with the same number of parameters. Chances are, you’d find that particle dark matter too is ruled out at 5 σ. It’s just that no one is dumb enough to make such a claim. When it comes to particle dark matter, astrophysicists will be quick to tell you galaxy dynamics involves loads of complicated astrophysics and it’s rather unrealistic that one parameter will account for the variety in any sample.

Without the comparison to particle dark matter, therefore, the only thing I learn from the Rodrigues et al paper is that a non-universal acceleration scale fits the data better than a universal one. And that I could have told you without even looking at the data.

Summary: I’m not impressed.

It’s day 12,805 in the war between modified gravity and dark matter and dark matter enthusiasts still haven’t found the battle field.

*Dude, I know that Newton isn’t Archimedes. I’m telling a story not giving a history lesson.

Ethan Siegel repeatedly makes the point that, whatever its dynamic successes, positing MOND at the expense of dark matter leaves unexplained certain aspects of the physical structure of the universe. Gravitational lensing; the relative abundance of photons & baryons; and the pattern of variations in the large-scale structure of the universe and the CMB, he says, are best explained if we affirm that something like 30% of the total energy of the universe is present in the form of matter. Of that, the known "normal" matter component is something like 5%, leaving 25% DM.

You (lately) appear to be a MOND-leaning agnostic on the subject; what is your take on these arguments?

My take is that this is irrelevant because it doesn't explain why modified gravity works so well on galactic scales. The theories are currently in no shape to say anything about structure formation or the CMB, that's correct. For what I know modified gravity works just fine with graviational lensing, so not sure what this is about.

I am not MOND-leaning. To begin with because we already know that MOND is wrong because it's only a non-relativistic limit. If anything I lean to somewhere between the two. Best,

An interesting question is how many modifications of Einstein's General Relativity that include MOND are still competing theories (to allow us to calculate galactic gravitational lensing, for instance).

I know, or think I know, that TeVeS has been ruled out by close-to-simultaneous observation of gravitational waves and an optical counterpart. But I do not know if a modification of this theory can explains the observation, or if there are other relativistic extensions of MOND that have not been ruled out yet.

I am not sure I understand why one would look for middle ground between MOND and dark matter. Surely they are different explanations for observations. To suggest the answer may be a bit of both seems to leave us with two mysteries rather than one. And poor Occam turning restlessly in his grave.

Hi,you wrote: "...the only thing I learn from the Rodrigues et al paper is that a non-universal acceleration scale fits the data better than a universal one. Summary: I’m not impressed. It’s day 12,805 in the war between modified gravity and dark matter and dark matter enthusiasts still haven’t found the battle field."

I am going to reach out to MOND half way. In the 19th century there was a proposal for a fix on the problem concerning the argument of periapsis or perihelion advance of Mercury. The argument was that Newtonian gravity force law should be F = Gmm/r^{2 – s}, where s is a small number. The only two force laws the maintain the semi-major axis invariant are F ~ r^2 and F ~ r^{-2}. This small deviation will cause a shift in the orbit that more or less agrees with the observed advance if one adjusts the small number s right.

This seems like an ugly fix to the problem that is very prosaic compared to general relativity. So it is, but the idea is not entirely without merit. Spacetime curvature means there are deficit angle around a closed curve that one parallel translates a vector. So the near circular orbit with radius r of a planet will has a small deficit angle, call that ε. The Ricci scalar curvature around this loop is then R ≈ ε/2πr^2. The curvature takes away a bit of the area of a Gaussian surface one integrates a for over, and to account for this so the integral is a fixed mass one must adjust the force law. It is not hard to see that s = 2ε. So this ugly fix pointed to something after all far deeper and profound.

I think that MOND or more likely the MOND-like fix of Eric Verlinde is similar to this. There may be something going on in general with the relationship between matter, and I think more specifically quantum matter-field, and spacetime curvatures. This will of course include dark matter, but I think ordinary matter as well.

Congratulations, Bee, on your fascinating, beautifully -- and clearly -- written Sci. Am. article. You've raised some very challenging issues without pretending to have all the answers. It certainly got me thinking.

I agree with Antonino. Between McGaugh and Nature Astronomy, who is more objective and credible? McGaugh has a horse in this race. An old Native American saying: if you discover you are riding a dead horse, the best thing to do is to dismount. But astrophysicists think no horse is too dead to beat. McGaugh should publish a rebuttal in Nature Astronomy. Let him resurrect a dead horse. That would be impressive.

Sabine, please say you are considering 'other alternatives' to these two?

I have been looking at contemporary physics for more than a year now, and have concluded that the following are 'already refuted models of reality':1) Special relativity, 2) General relativity, 3) Newtonian gravity, 4)black holes, 5) The big bang, 6) inflation, 7) speed-of-recession redshift, 8) an expanding universe, 9) dark matter, 10) dark energy,...

Getting my drift? The electric universe theory looks to me to replace all these models, without any difficulty. And without the need for time-bending, or dimension-multiplying, or any other 'imaginary mathematical physics'. Looked at this From the EU perspective, the floundering of contemporary physics is entirely explainable, even predictable.

I get the impression you didn't read the post. As I explained, the model has theoretical uncertainty that's not accounted for in the analysis, hence that the one-parameter fit isn't great is inconclusive. As I said, chances are that with such an analysis you can also rule out dark matter.

I thought Milgrom’s acceleration constant a0 (the zero should be subscripted, sorry) sounded like nonsense the first time I heard of it (from I think an article in Discovery magazine several years ago). Dark matter rapidly became the consensus explanation, and the Bullet Cluster seemed to verify it (according to popular accounts), but it has been going downhill since then. The data appear to be trying to tell us something new. "Modified Newtonian Mechanics" still sounds nonsensical, but maybe sometimes you have to take a few steps back to move forward (on a new path).

Could it be that we have found a place where discrete and continuous mathematics differ? (I was emboldened to see in the site's Twitter log that George Ellis might be on that same bandwagon with me, albeit in the First Class rather than Economy section.)

The theoretical uncertainty that's not accounted for in the analysis does not prove the one-parameter fit. Therefore, the null hypothesis cannot be rejected. As far as the data is concerned, there is no one-parameter fit. One cannot invoke a perceived anomaly to reject the null hypothesis. The anomaly has to be adequately explained and accounted for in order to fit data and hypothesis. This is what McGaugh ought to do.

A number of people have tried to post comments on this thread and are now complaining that they didn't appear. I want to remind everyone that I do not approve elaborations on your pet theories. This thread is to discuss the paper.

You have a misunderstanding there. McGaugh et al are observational astrophysicists. They don't produce hypotheses, they test them. They have merely analyzed the data and find there's a preferred acceleration scale in it.

Sure, someone who works on a theory for modified gravity should come up with more sophisticated models to fit the outliers. But I suspect that you wouldn't learn much from it because there isn't enough data for the outlying galaxies. You'd just end up fitting parameters to data. The interesting thing to learn here is thus that there *is* is a preferred acceleration scale in the data. The dark matter folks should try to explain that to begin with.

This whole debate between MOND and Dark Matter, or possibly something in between, is fascinating, and the premier scientific mystery of our time. Luckily, I managed to purchase the last copy of the August Scientific American at a local bookstore, which contains the article co-authored by Sabine and Stacy McGaugh. In this rural area very few outlets carry the magazine. Also began to print out the very long paper on MOND and Relativistic Extensions co-authored by Stacy McGaugh and Benoit Famaey, that was linked at Stacy's awesome Tritonstation website. Got some positively good reading to look forward to.

"It is a relativistic completion of MOND, that's what I constructed it for."

I found your blog post about this relativistic completion of MOND very enlightening.

A cosmology student told me cosmologists need particle dark-matter to get the evolution of the matter universe, i.e., galaxies, right. Now, I understand that fields and particles are two sides of the same coin in theoretical physics. But could the particle side of this relativistic completion of MOND eventually play the role of the particulate black matter in cosmology?

There's not really a war going on anymore; dark matter has decisively won. I'm an astronomy graduate student, and in every textbook, class, colloquium, and conference I'm aware of, dark matter is taken as a given while MOND is hardly mentioned. Maybe the victory is unfair or premature, but there's no doubt that it happened.

As for the paper, it's an interesting result, but I don't see it as evidence against dark matter. Normal matter and dark matter have been interacting gravitationally since the beginning of the universe. Gas falls into dark matter potential wells, cools, and form stars. The stars explode, and the ejecta pulls some dark matter along. There's so much interaction that it's not implausible normal matter traces dark matter in some way that you can write an equation for.

Of course the paper doesn't address strong evidence in favor of dark matter, like the Bullet Cluster, the CMB, gravitational lensing (which measures total mass), or the difficulty of forming large scale structure without dark matter. I hope someone someday can explain all of this without dark matter, but the possibility seems exceedingly remote.

I read an article in Astronomy magazine, written by Tyler, that talks about MOND and I understood that changing the Hubble constant would be the reason for the flat speed of galaxies, what do you think?

It is a false choice, this MOND/dark matter dichotomy. DM is a physical conjecture in which a proposed entity has only a gravitating effect and no other observable properties. It is useful for calculational purposes because it can be sprinkled in just the necessary amounts and locations to reconcile any discrepancy between a gravitational model and observed reality. It produces a non-empirical, which is to say unscientific, account of physical reality.

MOND is a heuristically derived mathematical fix to reconcile observed galactic rotation curves with those predicted by employing the Keplerian method. Unfortunately, there is no excuse for using the solar system derived Keplerian method to calculate galactic rotation curves. The Keplerian based model is a misrepresentation of galactic physics. Absent the Keplerian expectation curves, there is no need to mathematically tweak either GR or Newtonian dynamics.

Proper qualitative analysis of galactic systems would obviate the need for either "fix". More generally, a sound qualitative model is a necessary basis for any empirically verifiable quantitative model.

Is there a reason MOND and dark matter in the form of (primordial) black holes, or possibly neutrinos, couldn't both be correct? so MOND explains galaxy rotation curves, and the dark matter is all black holes, (or possibly neutrinos) which also explains CMB and large scale structure? maybe there's more neutrinos than standard big bang cosmology, and more black holes.

maybe the big bang has to be adjusted to explain (primordial) black holes, but there's no agreement on inflation either.

Sean s.: It hasn't been detected directly, but to me there's no difference between dark matter and something that acts exactly like dark matter (and not like modified gravity) in everything we measure, every model we produce, and every observation we make. It's more accurate to say we don't have a theoretical explanation for dark matter than to say we don't know if it exists.

Hi,concerning "To begin with because we already know that MOND is wrong because it's only a non-relativistic limit" - didn't Prof. Beckenstein (RIP)extended MOND to relativistic?Mentioning Beckenstein - shouldn't the "Hawking radiation" termed "Beckenstein radiation"? or at least "Beckenstein-Haking", since he was the first one to demonstrate that black holes heve Entropy => heat=> theu must radiate?Miki

Hi! I recently read yours and Dr. McGaughs article on dark matter in the August issue of Scientific American and came across a puzzler which happens frequently in discussions involving gravity. In the opening paragraphs, you assert “But Einstein’s general theory of relativity taught us that gravity is not a force and is instead caused by the curvature of space and time.” And yet, later in the article in a text box we have “This can occur because all forces, including gravity, are thought to be transmitted by a special type of particle.” which I assumed you were referring to the graviton, a hypothetical gauge boson thought to be the force carrier quantum of the gravitational field. My question is how can we solve the discrepancies between dark matter, MOND and general relativity when we haven’t yet resolved quantum gravity? Thank you for any clarification you could provide!r/ David Woodbury

The standard MOND model is based on a change in Newtonian dynamics for extremely small accelerations. It may also be seen as a change in gravitation for cases where GM/r (potential) or GM/r^2 (force) are very small. Either the 1/r and 1/r^2 law is changed by some tiny amount or there is some change in the gravitational coupling μ = GM so that μ = μ(r) according to some tiny variation. This is adjusted to account for how galaxies at large radii rotate almost as a solid disk.

MOND is then a sort of phenomenological tool and should not be seen as a fundamental theory of any sort. It also holds for a stationary galaxy. Situations such as the Bullet Cluster galaxy collision are problematic for MOND and as I read the cards MOND does not provide a decent fix for this.

Verlinde has proposed a model for how de Sitter spacetimes can have odd stress-energy tensors. With anti-de Sitter spacetime arc that connect to the boundary quantum entanglements of bulk graviational states have a one to one correlation with quantum states on the boundary. In this way AdS_n bulk gravity with a path integral sum over geometries Z = ∫D[g]e^{-iS[g]} is equal to the partition function sum over states = ∫D[ψ]e^{-iI[ψ]} for a quantum field CFT_{n-1} on the conformal boundary. With de Sitter spacetimes, which based on observation is very close to what we appear to exist in, odd things happen so that entanglements do not have this one to one relationship with the cosmological horizon. Erik Verlinde then proposes there is an odd emergent effect with this entanglement entropy force, which has some phenomenological similarities to what we call dark matter.

What Erik proposes is in some ways similar to the swampland of Cumrun Vafa. These are regions in or around the landscape where there is some sort of symmetry breaking or other process that results in gravity, say weak gravity we observe, that is not consistent with QFT in the dS. The boundary of the the AdS is an Einstein spacetime, which can be a de Sitter spacetime, that is free of local gravity. Gravity is not consistent with string theory in dS spacetime. Yet at least on a low energy basis with a weak limit there is gravity in our observable world. This might then mean we live in this swamp, or maybe the not so beautiful regions of the landscape --- think of a ghetto, where there is outwardly this appearance of something horribly amiss. What Erik proposes is then a possible phenomenology or maybe some fundamental theory that might fix the inconsistency of gravity existing in our observable dS cosmology.

I tend to think there may be some particle interpretation for this. It would be nice in the end if this sort of idea for dark matter had some particle basis to it. We are after all in a quantum world, and there is some relevancy to the old Dirac idea of a wave-particle duality.

Maybe dark matter is related to quantum gravity (some physicists think it is), but there is presently no particular reason to think so. The reference to particles is actually unnecessary. We just did this to avoid having to explain what a field is. A more correct but somewhat more difficult to understand statement is that both dark matter and modified gravity require the introduction of new fields (which, when quantized come with particles). We did this to explain why it's wrong to think that in modified gravity the center of the total gravitational pull must coincide with that of normal matter.

Yes, that's the idea. It's a kind of particle that forms a fluid and the fluid makes a phase-transition to a superfluid phase, which causes a long-range force that reproduces the MOND-law. This means in cases when the density contrast is small and average temperatures are large (early days in cosmology) then particle dark matter is a good description, but in cases where density contrast is high it's not (that's in galaxies). And if the gradients get too large, the superfluid approximation breaks down, so you can't use MOND in the solar system. (The latter point isn't really clear to me. It's one thing to say the approximation breaks down but another to figure out what is the correct theory.)

My misunderstanding is acknowledged. I thought McGaugh has a MOND hypothesis to replace the dark matter hypothesis. Thank you for clarifying that he has none. He merely observed that there is a preferred acceleration scale. Is it statistically significant to 4-sigma? If yes, theorists should formulate a MOND hypothesis from it. If not, the null hypothesis stands.

what if some researchers write a paper simulate the universe using MOND + primordial black hole dark matter (and possibly neutrinos) at 6x baryonic visible matter, and are able exactly reproduce the observed universe, from gravitational lensing to CMB to large scale structure, with MOND explaining galaxy rotation curves. these results pass peer review and are reproducible

If read right Rodrigues et al use flat statistics with hard boundaries instead of gaussian. Do this simulate the pre-selected model? I see as if they try to aim to the their most wanted conclusion... :)

Space Time said..."Are there any modified gravity proposals that are actually modified gravity, not just in name?"

to first order both QED and QCD and both Newtonian and relativistic gravity regard the sources as monopoles with corresponding 1/r potentials. While both QED and Yang-Mills include the 2D bivector as a second component of the two component spinor, the anomalous connection with the 1/r^2 potential associated monopole-bivector interactions (quantum Hall and Aharonov-Bohm effects come to mind) is not clearly understood in either particle physics or models of gravitation.

Quantum gravity requires a geometric wavefunction, requires inclusion of all eight geometric components (point, line, plane, and volume elements) of the 3D Pauli wavefunction of geometric Clifford algebra, the 'wavefunction of space' so to speak. Higher order corrections follow from including the 1/r^2 potentials of 'ficticious' forces (resulting motion is perpendicular to applied force - they can do no work, cannot communication energy/information, only the quantum phase of entanglement, itself not a single measurement observable) and including 1/r^3 potentials of dipole-dipole interactions.

also in response to SpaceTime's question, still puzzling about how Sabine's logarithmic potential plays. Can anyone help with this? It's a step on the way to a scale invariant potential, but having a hard time getting an intuitive sense of this

Sabine,We have recently published a paper (MNRAS2018; Astroph-1705.02918) discussing the “acceleration discrepancy” (AD) found in the analysis of McGaugh and collaborators, in the light of what we call the “Two-Component Virial Theorem”. This is a simplified extension of the usual Virial Theorem describing the equilibrium of a system composed by a spheroidal subsystem (e.g baryonic matter) embedded in a larger one (e.g a dark matter halo). We found that such a modelling naturally explains the AD as a consequence of the usual gravitational interaction between the two subsystems.

Is it statistically significant to 4-sigma? McGaugh answered my question in his blog post, The Acceleration Scale in the Data. To quote: “if these results really do indicate the action of a single universal force law, then it should be possible to fit each individual galaxy… Does it work for the entirety of SPARC?... the answer is yes… There are some inevitable goofballs; this is astronomy after all. But by and large, it works much better than I expected – the goof rate is only about 10%”

The evidence for his “universal force law” is more likely than picking a Queen in a deck of cards. Sorry Stacy that level of evidence is not acceptable even in psychic card reading tests, but it would be in astrology. Stacy warned us: Do not bet against MOND. I think it’s safe to bet the psychic card reader is fake.

"what the heck is going on?" The universe is cyclic in Mass and Time. That merely requires that the Temporal Curvature term be considered an imaginary quantity.. just like in every other field of physics, the representation geometry is FUNDAMENTAL. (not just a "visual aid")